Three-sided hypothesis testing: simultaneous testing of superiority, equivalence and inferiority

Stat Med. 2010 Sep 10;29(20):2117-25. doi: 10.1002/sim.4002.


We propose three-sided testing, a testing framework for simultaneous testing of inferiority, equivalence and superiority in clinical trials, controlling for multiple testing using the partitioning principle. Like the usual two-sided testing approach, this approach is completely symmetric in the two treatments compared. Still, because the hypotheses of inferiority and superiority are tested with one-sided tests, the proposed approach has more power than the two-sided approach to infer non-inferiority or non-superiority. Applied to the classical point null hypothesis of equivalence, the three-sided testing approach shows that it is sometimes possible to make an inference on the sign of the parameter of interest, even when the null hypothesis itself could not be rejected. Relationships with confidence intervals are explored, and the effectiveness of the three-sided testing approach is demonstrated in a number of recent clinical trials.

Publication types

  • Comparative Study
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Biostatistics
  • Carotid Stenosis / mortality
  • Carotid Stenosis / surgery
  • Clinical Trials as Topic / statistics & numerical data*
  • Colonic Neoplasms / mortality
  • Colonic Neoplasms / surgery
  • Confidence Intervals
  • Diabetes Mellitus, Type 2 / drug therapy
  • Endarterectomy, Carotid
  • Humans
  • Models, Statistical*
  • Pulmonary Disease, Chronic Obstructive / drug therapy
  • Pulmonary Disease, Chronic Obstructive / mortality
  • Randomized Controlled Trials as Topic / statistics & numerical data
  • Stents
  • Therapeutic Equivalency